A dissection puzzle
T. Sillke asks for dissections of two heptominoes into squares. |
A Pentominoes Project from Belgium
Secondary School project about pentominoes and fun with math. History, descriptions, and problems. Bi-monthly pentomino competition. A solver is available. [English, French, Dutch] |
A Puzzle by Enrich Friedman
Every square can be dissected into L-ominoes. Can every Pythagorean square? Conjecture needs proof. |
Animal enumerations
Enumeration on regular tilings of the Euclidean and Hyperbolic planes. |
Anna's Pentomino Page
Anna Gardberg makes pentominoes out of sculpey and agate. |
Arnab's Pentominos Puzzle
Fast Pentominos puzzle solver, works on DOS/Windows platform. Free downloads. |
Blocking polyominos
Rodolfo Kurchan asks, for each k, what is the smallest polyomino such that k copies can form a blocked pattern. With solutions. |
Canonical polygons
Ronald Kyrmse investigates grid polygons in which all side lengths are one or sqrt(2). |
Christopher Monckton's Eternity Puzzle
Rules, the solution by Alex Selby and Oliver Riordan, other resources and links. The puzzle is made up of 209 pieces of polydrafters, each one is a combination of 12-30/60/90 triangles. |
Counting Horizontally Convex Polyominoes
Journal of Integer Sequences, Vol. 2 (1999), Article 99.1.8. Defines and counts horizontal convexity. |
Cynthia Lanius' Lesson: Polyominoes Introduction
From tetris to hexominoes, Cynthia explains them in color. |
Dancing links
Don Knuth discusses implementation details of polyomino search algorithms. |
Eithan's Pentominoes-3D Applet Solver
Solves given Pentominoes 3D puzzles. Solution is displayed in 3-D with disassembly and rotations. General information and data. [requires Java] |
Equilateral pentagons
Jorge Luis Mireles Jasso investigates these polygons and dissects various polyominos into them. Animations show cases of infinite solutions. |
Eternity Page
Alex Selby's page with a description of his solution method, with illustrations in .png and .pdf files. |
Flexagons
Folded paper polyiamonds which can be unfolded to show hidden faces. Make interesting school projects. |
Flexagons
Conrad and Hartline's 1962 article on Flexagons. |
Gamepuzzles
Polyomino and polyform games and puzzles manufactured by Kadon Enterprises Inc. |
George Huttlin's Puzzle Page
George Huttlin shares some ramblings in the world of polyominoes. |
Gerard's Pentomino Page
Illustrates the 12 shapes. symmetrical combinations. |
Gerard's Universal Polyomino Solver
Computes from 1 to 3.38 billion solutions with graphic display to each of the 60+ problems of different sizes and shapes. Pieces vary from pentominoes to heptominoes, sometimes in combination. Table summarizes properties and example solution of each prob |
Golygons
Harry J. Smith's explains polyominoes with consecutive integer side lengths. |
Golygons by Mathworld
What they are, and how to find them. |
Harold McIntosh's flexagon papers
Including copies of the original 1962 Conrad-Hartline papers. Abstract, html-pages, or .pdf documents. |
Henri Picciotto's Geometric Puzzles in the Classroom
Polyform puzzle lessons for math educators to use with their students, including polyominoes, supertangrams, and polyarcs. |
Hepto
Some packings of the 108 heptominoes (with unit thickness) into various blocks. |
hexiamonds
George Huttlin explains and illustrates these shapes composed of 6 equilateral triangles, which in turn tiles different forms. |
Hyperbolic planar tessellations
Don Hatch's page on hyperbolic tesselations with numerous illustrations. |
Information on Pentomino Puzzles
At the Combinatorial Object Server. |
Isoperimetric polygons
Livio Zucca tiles polygons of equal perimeter, or isoperiploes. |
Java pentominoes
Thery families web site with pentomino solver. (English/French)[Java]. |
Knight's Move Tessellations
Dan Thomasson looks at tesselations with numerous unexpected shapes traced out by knight moves. |
Lego Pentominos
Eric Harshbarger. This puzzle maker says that the hard part was finding legos in enough different colors. |
Livio Zucca's polyomino-covered cube
Colorful illustrations demonstrate how closed surfaces could be covered by polyominoes. |
Logical Art and the Art of Logic
Pentomino pictures, software and other resources by Guenter Albrecht-Buehler. |
Mathforum : a pentomino problem
from the Geometry Forum. Lists the pentominoes; fold them to form a cube; play a pentomino game. (project of the month, 1995) |
Mathforum : minimal domino tiling
Tiling a square without cutting it into two.(Problem of the week 826, Spring 1997) |
Mathforum : Tiling rectangles from ell
Stan Wagon asks which rectangles can be tiled with an ell-tromino. |
Maximum convex hulls of connected systems of segments and of polyominoes
Bezdek, Brass, and Harborth. Abstract to an article which places bounds on the convex area needed to contain a polyomino. (Contributions to Algebra and Geometry Volume 35 (1994), No. 1, 37-43.) |
Miroslav Vicher's Puzzles Pages
Polyforms (polyominoes, and polyiamonds) graphics, tables and resources (English/Czech). |
my polyomino page
Michael Reid's numerous articles on polyominoes and tilnig, with references and links. |
Packing Ferrers Shapes
Alon, Bóna, and Spencer show that one can't cover very much of an n by p(n) rectangle with staircase polyominoes (where p(n) is the number of these shapes). |
Packing Polyominoes
Erich Friedman's Introduction to a variety of packing and tiling problems. |
Packing polyominoes
Mark Michell investigates packing pentominoes into rectangles of various non-integer aspect ratios in order to obtain the largest possible pieces using straight cuts. |
Pairwise touching hypercubes
Erich Friedman's problem of the month asks how to partition the unit cubes of an a*b*c-unit rectangular box into as many connected polycubes as possible with a shared face between every pair of polycubes. Answers provided. |
Pentamini pentaminos pentominoes
A container of mathematical games, gadgets and software. (English/Italian) |
Pento
Amamas Software offers a pentomino solving software. |
Pento-Mania
Pentomino based puzzle game lets children solve and create geometric puzzles. Win32 software, try or buy. |
Pentomino applet
Fill up a given area using pentomino shapes, rotating and flipping them. Three levels of difficulty.[Java]. |
Pentomino Applet
Rujith de Silva's applet puzzle offers games of four different sized rectangles. [Java] |
Pentomino Covers
Problems on minimal covers. |
Pentomino dissection of a square annulus
From Scott Kim's Inversions Gallery. |
Pentomino HungarIQa
Kati presents a pentomino puzzle using poly-rhombs instead of poly-squares. [English/French/German/Hungarian] |
Pentomino Relationships
Symmetries in the families of rectangular solutions. |
Pentomino, Homepage
Lorente Philippe's site describes the building blocks, nomenclature, solutions, and numerous games. (French/English) |
Pentominoes
Expository paper by R. Bhat and A. Fletcher. Covers pre-Golomb discoveries. the triplication problem and other aspects. |
Pentominoes - an introduction
Centre for Innovation in Mathematics Teaching presents colourful examples of many tiling problems, duplication, triplication, etc. |
Pentominopuzzles.
Pentomino solver with download. Windows 95 and later required. [German/English] |
Pentominos
Graphics problems, solutions (including animated GIF) and links. (English/German through main page) |
Pentominos
B. Berchtold's applet helps tile a 6x10 rectangle. [German] |
Pentominos Puzzle Solver
David Eck's graphical solver applet uses recursive technique. Source code available. [Java] |
Polyform and dissection puzzle links
Christian Eggermont's link page. |
Polyform spirals
Jorge Luis Mireles explains finite and infinite spirals made up of polyforms. |
Polyforms
. Ed Pegg Jr.'s site has pages on tiling, packing, and related problems involving polyominos, polyiamonds, polyspheres, and related shapes. |
Polygon Puzzle
Open source polyomino and polyform placement solitaire game. |
Polyiamond exclusion
Colonel Sicherman asks what fraction of the triangles need to be removed from a regular triangular tiling of the plane, in order to make sure that the remaining triangles contain no copy of a given polyiamond. |
Polyiamonds
Mathforum. This Geometry problem of the week asks whether a six-point star can be dissected to form eight distinct hexiamonds. |
Polyomino and Polyhex Tiling
Joseph Myer's tables of polyominoes and of polyomino tilings, in Postscript format. |
Polyomino applet
Wil Laan's applet searches for solution of packing hexominoes into more than 45 different shapes.[Java] |
Polyomino enumeration
K. S. Brown examines the number of polyominoes up to order 12 for various cases involving rotation or reflections. Equations linking the cases are proposed. |
Polyomino Fuzion game
Puzzles using pentominoes and hexominoes. Fuzion, game that designs and (semi-)automatically finds solutions. Links. |
Polyomino problems and variations of a theme
Jankok presents information about filling rectangles, other polygons, boxes, etc., with dominoes, trominoes, tetrominoes, pentominoes, solid pentominoes, hexiamonds, and whatever else people have invented as variations of a theme. References included. |
Polyomino tiling
. Joseph Myers classifies the n-ominoes up to n=15 according to how symmetrically they can tile the plane. |
Polyominoes
Describes a numerical invariant that can be used to classify polyominoes. |
Polyominoes
Introduction to Tetrominoes, Pentominoes, Hexominoes, Heptominoes, Octominoes, Fixed (translation only) Polyominoes. Numerous Links. |
Polyominoes: Theme and Variations
A brief essay with some references. |
Polyominoids
Jorge Luis Mireles Jasso presents connected sets of squares in a 3d cubical lattice. Includes a Java applet as well as non-animated description. |
Polypolygon tilings
S. Dutch discusses polyominoes, poliamonds, and polypolygons with special attention to tiling characteristics. |
Primes of a 14-omino
Michael Reid shows that a 3x6 rectangle with a 2x2 bite removed can tile a (much larger) rectangle. It is open whether it can do this using an odd number of copies. |
Puzzle Fun
Newsletter edited by Rodolfo Kurchan about pentominoes and other math problems. |
Random domino tiling of an Aztec diamond
Matthew Blum demonstrates the properties of random domino tiling of an Aztec diamond. Interactive graphics display. |
Rectifiable polyomino
Karl Dahlke explains and demonstrates tiling. Includes C-program source. |
Schröder Triangles, Paths, and Parallelogram Polyominoes
A paper on their enumeration by Elisa Pergola and Robert A. Sulanke. |
Six squares problem
This Geometry Forum problem of the week asks for the number of different hexominoes, and for how many of them can be folded into a cube. |
Solomon W. Golomb
Home Page of the inventor of polyominoes. Includes biography, black and white picture, research interests and publications list. |
Soma cube applet
Mehta & Ward Alberg explains the soma cube and provides an applet for practice. Source codes included. [Java] |
Somatic
A solver for arbitrary polyomino and polycube puzzles. Binary code and source downloads available. |
sqfig and sqtile
Eric Laroche presents computer programs for generating polyominoes and polyomino tilings. Includes source codes in C, and binaries. |
square into similar triangles
T.Sillke discusses the dissection problem. |
Taniguchi's Programs
Windows software to solve polyiamond and sliding block puzzles. |
Tesselating locking polyominos
Bob Newman examines the history of the subject and presents his minimal solutions. |
The Geometry Junkyard: Polyominoes
Numerous links, sorted alphabetically. |
The Mathematics of Polyominoes
Kevin Gong's home page includes articles, programs for Mac, Win and Java. |
The mathematics of polyominoes
Kevin Gong offers download of his polyominoes games shareware for Windows and Mac. 100 boards are included. A Java version is in the works. |
The Pentomino-Dictionary by Gilles Esposito-Farèse
English words that can be written using the pentomino name letters FILNPTUVWXYZ and other related curiosities, including a homage to Georges Perec. (English/French). |
The Poly Pages
About various polyforms - polyominoes, polyiamonds, polycubes, and polyhexes. |
The Soma Cube
Soma-solving program in QBASIC by Courtney McFarren. |
The three dimensional polyominoes of minimal area
L. Alonso and R. Cert's abstract of a paper published in vol. 3 of the Elect. J. Combinatorics. Full paper available in different formats (.pdf, postscript, tex etc). |
The tiling puzzle games of OOG
Mr. Confetti presents a Windows and Java game for tangrams, polyominoes, and polyhexes. |
Thorleif's SOMA Page
SOMA puzzle site with graphics, newsletter and software. |
Three nice pentomino coloring problems
Alexandre Owen Muñiz presents the Icehouse set which lends itself to different polyomino coloring games. |
Tiling a square with eight congruent polyominoes
Michael Reid's abstract of a paper in the "Journal of Combinatorial Theory, Series A". |
Tiling and Packing Results of Torsten Sillke
Polyominoes, polycubes and polyspheres. |
Tiling of Pythagorean triplets
Joe Fields suggests that L-decomposition of squares of Pythagorean triplets could always be tiled. |
Tiling rectangles and half strips with congruent polyominoes
Michael Reid's abstract of paper in the "Journal of Combinatorial Theory, Series A". |
Tiling stuff
Jonathan King examines problems of determining whether a given rectangular brick can be tiled by certain smaller bricks. Includes numerous articles in .pdf format. |
Tiling UROP Homepage
Undergraduate Research Project in Random Tilings. |
Tiling with notched cubes
Robert Hochberg and Michael Reid exhibit an unboxable reptile: a polycube that can tile a larger copy of itself, but can't tile any rectangular block. Abstract of article to "Discrete Mathematics". |
Unbalanced anisohedral tiling
Joseph Myers and John Berglund found a polyhex that must be placed in two different ways in a tiling of a plane, such that one placement occurs twice as often as the other. |
Unbeatable Tetris
Java applet demonstres that this tetromino-packing game is a forced win for the side dealing the tetrominoes. Complete with mathematical proof. [Java] |
Unfolding the tesseract
Peter Turney lists the 261 polycubes that can be folded in four dimensions to form the surface of a hypercube, and provides animations of the unfolding process. |
What is a Golygon?
Harry Smith describes Dr. Dewdney's article in the July 1990 Scientific American's Mathematical Recreations column. |
Xominoes
Livio Zucca finds a set of markings for the edges of a square that lead to exactly 100 possible tiles, and asks how to fit them into a 10x10 grid. |
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